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Mandelbrot set for fractal n-gons and zeros of power series 分形正圆和幂级数零点的曼德布罗特集
IF 0.6 4区 数学
Topology and its Applications Pub Date : 2024-04-16 DOI: 10.1016/j.topol.2024.108918
Yuto Nakajima
{"title":"Mandelbrot set for fractal n-gons and zeros of power series","authors":"Yuto Nakajima","doi":"10.1016/j.topol.2024.108918","DOIUrl":"https://doi.org/10.1016/j.topol.2024.108918","url":null,"abstract":"<div><p>We give a framework to study the connectedness of the set of zeros of power series with coefficients in a finite subset <span><math><mi>G</mi><mo>⊂</mo><mi>C</mi></math></span>. We prove that the set of zeros in the unit disk is connected and locally connected if some graph on the set <em>G</em> of coefficients is connected. Furthermore, we apply this result to the study of the Mandelbrot set <span><math><msub><mrow><mi>M</mi></mrow><mrow><mi>n</mi></mrow></msub></math></span> for fractal <em>n</em>-gons. We prove that <span><math><msub><mrow><mi>M</mi></mrow><mrow><mi>n</mi></mrow></msub></math></span> is connected and locally connected for any <em>n</em>.</p></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-04-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140633530","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Sensitivity in hyperspatial and product systems via Furstenberg families 通过弗斯滕伯格族实现超空间和积系统中的敏感性
IF 0.6 4区 数学
Topology and its Applications Pub Date : 2024-04-16 DOI: 10.1016/j.topol.2024.108907
Arpit Mahajan , Rahul Thakur , Ruchi Das
{"title":"Sensitivity in hyperspatial and product systems via Furstenberg families","authors":"Arpit Mahajan ,&nbsp;Rahul Thakur ,&nbsp;Ruchi Das","doi":"10.1016/j.topol.2024.108907","DOIUrl":"https://doi.org/10.1016/j.topol.2024.108907","url":null,"abstract":"<div><p>In this paper, we study the notions of <span><math><mi>F</mi></math></span>-sensitivity, multi-<span><math><mi>F</mi></math></span>-sensitivity and <span><math><mo>(</mo><msub><mrow><mi>F</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><msub><mrow><mi>F</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>)</mo></math></span>-sensitivity in dynamical systems defined on Hausdorff uniform spaces. It is shown that how these notions carry over to hyperspatial and product dynamical systems, and vice versa. We also obtain some sufficient conditions for a dynamical system to be <span><math><mi>F</mi></math></span>-sensitive. Some examples showing the necessity of the conditions taken in our results are also presented.</p></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-04-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140558855","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Non-cut ordered arcs of the hyperspace of subcontinua 子洲超空间的非切割有序弧
IF 0.6 4区 数学
Topology and its Applications Pub Date : 2024-04-10 DOI: 10.1016/j.topol.2024.108908
José G. Anaya, David Maya
{"title":"Non-cut ordered arcs of the hyperspace of subcontinua","authors":"José G. Anaya,&nbsp;David Maya","doi":"10.1016/j.topol.2024.108908","DOIUrl":"https://doi.org/10.1016/j.topol.2024.108908","url":null,"abstract":"<div><p>Let <span><math><mi>C</mi><mo>(</mo><mi>X</mi><mo>)</mo></math></span> be the hyperspace of all subcontinua of a continuum <em>X</em> topologized by Hausdorff metric. For a non-empty closed subset <em>A</em> of a continuum <em>X</em>, consider the following properties: <em>A</em> is a strong non-cut subset, non-block subset, weak non-block subset, shore subset, not a strong center, and non-cut subset of <em>X</em>. The aim of this paper is to study the conditions under which an ordered arc from a singleton to a proper subcontinuum of a continuum <em>X</em> has one of these properties in <span><math><mi>C</mi><mo>(</mo><mi>X</mi><mo>)</mo></math></span>.</p></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-04-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140558819","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On topological entropy (chaos) realized far from fixed point 论远离定点的拓扑熵（混沌）的实现
IF 0.6 4区 数学
Topology and its Applications Pub Date : 2024-04-10 DOI: 10.1016/j.topol.2024.108910
Ewa Korczak Kubiak, Ryszard J. Pawlak, Justyna Poprawa
{"title":"On topological entropy (chaos) realized far from fixed point","authors":"Ewa Korczak Kubiak, Ryszard J. Pawlak, Justyna Poprawa","doi":"10.1016/j.topol.2024.108910","DOIUrl":"https://doi.org/10.1016/j.topol.2024.108910","url":null,"abstract":"In many papers, the concept of chaos is associated with positive topological entropy. The points around which chaos is concentrated are also often examined. In this paper we distinguish places of chaos generation and its realization. Moreover, we will consider the possibility of approximation of continuous function by functions having full entropy point (there is chaos generated by any neighbourhood of it) but simultaneously is not a focal entropy point (chaos is realized at some distance from the considered point).","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-04-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140594351","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Hurewicz and Dranishnikov-Smith theorems for asymptotic dimension of countable approximate groups 可数近似群渐近维度的 Hurewicz 和 Dranishnikov-Smith 定理
IF 0.6 4区 数学
Topology and its Applications Pub Date : 2024-04-10 DOI: 10.1016/j.topol.2024.108905
Tobias Hartnick , Vera Tonić
{"title":"Hurewicz and Dranishnikov-Smith theorems for asymptotic dimension of countable approximate groups","authors":"Tobias Hartnick ,&nbsp;Vera Tonić","doi":"10.1016/j.topol.2024.108905","DOIUrl":"https://doi.org/10.1016/j.topol.2024.108905","url":null,"abstract":"<div><p>We establish two main results for the asymptotic dimension of countable approximate groups. The first one is a Hurewicz type formula for a global morphism of countable approximate groups <span><math><mi>f</mi><mo>:</mo><mo>(</mo><mi>Ξ</mi><mo>,</mo><msup><mrow><mi>Ξ</mi></mrow><mrow><mo>∞</mo></mrow></msup><mo>)</mo><mo>→</mo><mo>(</mo><mi>Λ</mi><mo>,</mo><msup><mrow><mi>Λ</mi></mrow><mrow><mo>∞</mo></mrow></msup><mo>)</mo></math></span>, stating that <span><math><mi>asdim</mi><mspace></mspace><mi>Ξ</mi><mo>≤</mo><mi>asdim</mi><mspace></mspace><mi>Λ</mi><mo>+</mo><mi>asdim</mi><mo>(</mo><msub><mrow><mo>[</mo><mi>ker</mi><mo>⁡</mo><mi>f</mi><mo>]</mo></mrow><mrow><mi>c</mi></mrow></msub><mo>)</mo></math></span>. This is analogous to the Dranishnikov-Smith result for groups, and is relying on another Hurewicz type formula we prove, using a 6-local morphism instead of a global one. The second result is similar to the Dranishnikov-Smith theorem stating that, for a countable group <em>G</em>, asdim <em>G</em> is equal to the supremum of asymptotic dimensions of finitely generated subgroups of <em>G</em>. Our version states that, if <span><math><mo>(</mo><mi>Λ</mi><mo>,</mo><msup><mrow><mi>Λ</mi></mrow><mrow><mo>∞</mo></mrow></msup><mo>)</mo></math></span> is a countable approximate group, then asdim Λ is equal to the supremum of asymptotic dimensions of approximate subgroups of finitely generated subgroups of <span><math><msup><mrow><mi>Λ</mi></mrow><mrow><mo>∞</mo></mrow></msup></math></span>, with these approximate subgroups contained in <span><math><msup><mrow><mi>Λ</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span>.</p></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-04-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140553996","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
The admissible monomial bases for the polynomial algebra of five variables in some types of generic degrees 五变量多项式代数在某些通用度类型中的可容许单项式基数
IF 0.6 4区 数学
Topology and its Applications Pub Date : 2024-04-10 DOI: 10.1016/j.topol.2024.108909
Nguyễn Sum
{"title":"The admissible monomial bases for the polynomial algebra of five variables in some types of generic degrees","authors":"Nguyễn Sum","doi":"10.1016/j.topol.2024.108909","DOIUrl":"https://doi.org/10.1016/j.topol.2024.108909","url":null,"abstract":"<div><p>Let <span><math><msub><mrow><mi>P</mi></mrow><mrow><mi>k</mi></mrow></msub></math></span> be the graded polynomial algebra <span><math><msub><mrow><mi>F</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>[</mo><msub><mrow><mi>x</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><msub><mrow><mi>x</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>,</mo><mo>…</mo><mo>,</mo><msub><mrow><mi>x</mi></mrow><mrow><mi>k</mi></mrow></msub><mo>]</mo></math></span> over the prime field of two elements, <span><math><msub><mrow><mi>F</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span>, with the degree of each <span><math><msub><mrow><mi>x</mi></mrow><mrow><mi>i</mi></mrow></msub></math></span> being 1. We study the <em>hit problem</em>, set up by Frank Peterson, of finding a minimal set of generators for <span><math><msub><mrow><mi>P</mi></mrow><mrow><mi>k</mi></mrow></msub></math></span> as a module over the mod-2 Steenrod algebra, <span><math><mi>A</mi></math></span>. In this paper, we explicitly determine a minimal set of <span><math><mi>A</mi></math></span>-generators for <span><math><msub><mrow><mi>P</mi></mrow><mrow><mn>5</mn></mrow></msub></math></span> in the case of the generic degrees <span><math><mi>n</mi><mo>=</mo><msup><mrow><mn>2</mn></mrow><mrow><mi>d</mi><mo>+</mo><mn>1</mn></mrow></msup><mo>−</mo><mn>1</mn></math></span> and <span><math><mi>n</mi><mo>=</mo><msup><mrow><mn>2</mn></mrow><mrow><mi>d</mi><mo>+</mo><mn>1</mn></mrow></msup><mo>−</mo><mn>2</mn></math></span> for all <span><math><mi>d</mi><mo>⩾</mo><mn>6</mn></math></span>.</p></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-04-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140554588","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Transitivity in nonautonomous systems generated by a uniformly convergent sequence of maps 由均匀收敛的映射序列生成的非自治系统中的传递性
IF 0.6 4区 数学
Topology and its Applications Pub Date : 2024-04-10 DOI: 10.1016/j.topol.2024.108904
Michaela Mlíchová, Vojtěch Pravec
{"title":"Transitivity in nonautonomous systems generated by a uniformly convergent sequence of maps","authors":"Michaela Mlíchová,&nbsp;Vojtěch Pravec","doi":"10.1016/j.topol.2024.108904","DOIUrl":"https://doi.org/10.1016/j.topol.2024.108904","url":null,"abstract":"<div><p>Let <span><math><mo>(</mo><mi>X</mi><mo>,</mo><mi>d</mi><mo>)</mo></math></span> be a metric space and <span><math><msub><mrow><mi>f</mi></mrow><mrow><mn>1</mn><mo>,</mo><mo>∞</mo></mrow></msub><mo>=</mo><msubsup><mrow><mo>{</mo><msub><mrow><mi>f</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>}</mo></mrow><mrow><mi>i</mi><mo>=</mo><mn>0</mn></mrow><mrow><mo>∞</mo></mrow></msubsup></math></span> be a sequence of continuous maps <span><math><msub><mrow><mi>f</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>:</mo><mi>X</mi><mo>→</mo><mi>X</mi></math></span> such that <span><math><mo>(</mo><msub><mrow><mi>f</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>)</mo></math></span> converges uniformly to a continuous map <em>f</em>. We investigate which conditions ensure that the transitivity of functions <span><math><msub><mrow><mi>f</mi></mrow><mrow><mi>n</mi></mrow></msub></math></span> or the transitivity of the nonautonomous system <span><math><mo>(</mo><mi>X</mi><mo>,</mo><msub><mrow><mi>f</mi></mrow><mrow><mn>1</mn><mo>,</mo><mo>∞</mo></mrow></msub><mo>)</mo></math></span> is inherited to the limit function <em>f</em> and vice versa. Such problem has been studied for instance by A. Fedeli, A. Le Donne or J. Li who give different sufficient condition for inheriting of transitivity from <span><math><msub><mrow><mi>f</mi></mrow><mrow><mi>n</mi></mrow></msub></math></span> to <em>f</em>. In this paper we give a survey of known result relating to this problem and prove new results concerning transitivity.</p></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-04-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140558818","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Topological spaces satisfying a closed graph theorem 满足封闭图定理的拓扑空间
IF 0.6 4区 数学
Topology and its Applications Pub Date : 2024-04-09 DOI: 10.1016/j.topol.2024.108903
Dominikus Noll
{"title":"Topological spaces satisfying a closed graph theorem","authors":"Dominikus Noll","doi":"10.1016/j.topol.2024.108903","DOIUrl":"https://doi.org/10.1016/j.topol.2024.108903","url":null,"abstract":"<div><p>We discuss topological versions of the closed graph theorem, where continuity is inferred from near continuity in tandem with suitable conditions on source or target spaces. We seek internal characterizations of spaces satisfying a closed graph theorem, and we compare closed graph and open mapping spaces.</p></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-04-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140558817","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Lipschitz classification of Bedford-McMullen carpets with locally uniform horizontal fibers 具有局部均匀水平纤维的贝德福德-麦克马伦地毯的 Lipschitz 分类
IF 0.6 4区 数学
Topology and its Applications Pub Date : 2024-04-09 DOI: 10.1016/j.topol.2024.108906
Liang-yi Huang , Yuan Zhang
{"title":"Lipschitz classification of Bedford-McMullen carpets with locally uniform horizontal fibers","authors":"Liang-yi Huang ,&nbsp;Yuan Zhang","doi":"10.1016/j.topol.2024.108906","DOIUrl":"10.1016/j.topol.2024.108906","url":null,"abstract":"<div><p>It is well known that the Hausdorff dimension and box dimension of a Bedford-McMullen carpet coincide if and only if the carpet has uniform horizontal fibers. Yang et al. <span>[17]</span> gave a complete Lipschitz classification of such carpets which are totally disconnected and possessing vacant rows. In this paper, we show that if we replace the uniform horizontal fibers condition by a locally uniform horizontal fibers condition, the conclusions of Yang et al. still hold.</p></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-04-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140594350","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A property equivalent to being semi-Kelley 相当于半凯利的特性
IF 0.6 4区 数学
Topology and its Applications Pub Date : 2024-04-08 DOI: 10.1016/j.topol.2024.108901
Mauricio Chacón-Tirado, María de J. López, Ivon Vidal-Escobar
{"title":"A property equivalent to being semi-Kelley","authors":"Mauricio Chacón-Tirado,&nbsp;María de J. López,&nbsp;Ivon Vidal-Escobar","doi":"10.1016/j.topol.2024.108901","DOIUrl":"10.1016/j.topol.2024.108901","url":null,"abstract":"<div><p>We present a property equivalent to the property of being semi-Kelley. Using this equivalence we prove that being semi-Kelley is a hereditary property for atriodic continua. We prove that semi-Kelley remainders are atriodic, moreover, we prove that semi-Kelley continua are semi-Kelley remainders for chainable continua, circularly chainable continua, and arc continua, and we give an example of an atriodic Kelley continuum which is a semi-Kelley remainder and not a Kelley remainder. We also prove that hereditarily semi-Kelley dendroids are smooth.</p></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-04-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140594451","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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